The orthogonal trajectories to a family of curves are the curves that intersect each member of the family at a perfectly perpendicular angle. So given a family of curves, you can change the value of the constant in the equation that models the family, to create a family of many curves, and then sketch the family in the plane.

Read MoreDifferential equations are usually classified into two general categories: partial differential equations, which are also called partial derivatives, and ordinary differential equations.

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